Engineering complex mathematical models in systems biology with Modelica using the example of the human cardiovascular system

Abstract

Biological systems are complex and full of interconnected feedback loops, which require going beyond reductionist endeavors to map the genome, transcriptome, and proteome and consider the whole system instead. This is the goal of systems biology, and it often involves the integration of multiple descriptions of biological systems at different scales of time and space. Since predictions about such complex systems are hard to make, mathematical simulations are used to quantitatively assess the phenomena under study. However, most mathematical models of biological systems are unfit for the sort of hierarchical composition required for this task both due to their structure and due to the programming or modeling language used. In engineering, systems of much larger size and similar complexity have been successfully modeled using the language Modelica, which is largely unknown in systems biology. This dissertation therefore asks if Modelica can be used to tackle the challenges of multi-scale modeling in systems biology. In place of the vast amount of biological models available, the dissertation focuses on models of the cardiovascular system, since this is an active and relevant field of research that showcases a lot of the typical complexity of biological systems. To assess the benefits of Modelica for systems biology, I first establish a set of requirements for modeling languages in systems biology in general by examining the properties of a subsystem in detail. I assess whether Modelica fulfills these requirements using models of the human baroreflex, the Hodgkin-Huxley model of the squid giant axon, and a one-dimensional model of the human atrioventricular node. As there are other languages that aim to solve similar issues, I then contrast their abilities with those of Modelica. This bridges to a broader investigation of the benefit of software engineering techniques in general, such as object orientation, structured documentation, or unit testing. Finally, I discuss and provide some improvements for the usability of Modelica in a biological context. The results of this dissertation indicate that Modeling languages used for systems biology should be modular, declarative, human-readable, open, graphical, and hybrid. From all investigated language candidates, Modelica fulfills these requirements to the fullest extent. Using other languages is possible, but brings drawbacks either in modularity, openness, or the graphical representation of models. However, SBML and CellML, which are recommended standard languages in systems biology, have the clear benefit of including domain-specific features such as semantic annotation using ontologies, and they also benefit from a high acceptance and interoperability with other tools in the community. Regardless of the concrete language, software engineering techniques should be applied to mathematical modeling similar to other pieces of software. Among other benefits, this could actually guarantee that the methods of a simulation study are reproducible. In the case of Modelica, this means that the language has to fit better into a typical software engineering workflow, which can be achieved by separate tools for code editing, vector graphics editing, and structured documentation, which are provided as part of this dissertation. At the bottom line, Modelica is not the perfect solution to every problem of systems biology, but at the very least it is a great source of inspiration that should either be used as the basis of or be partly incorporated into future languages.